Connexions

You are here: Home » Content » Impulse-Invariant Design
Content Actions
Lenses

What is a lens?

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

This content is ...
Affiliated with (?)
This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • This module is included inLens: Rice University OpenCourseWare
    By: OpenCourseWare ConsortiumAs a part of collection:"Digital Filter Design"

    Click the "Rice University OCW" link to see all content affiliated with them.

    Rice University OCW
Tags

(?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Impulse-Invariant Design

Module by: Douglas L. Jones

Pre-classical, adhoc-but-easy method of converting an analog prototype filter to a digital IIR filter. Does not preserve any optimality.
Impulse invariance means that digital filter impulse response exactly equals samples of the analog prototype impulse response: n:hn= h a nT n h n h a n T How is this done?
The impulse response of a causal, stable analog filter is simply a sum of decaying exponentials: H a s= b 0 + b 1 s+ b 2 s2+...+ b p sp1+ a 1 s+ a 2 s2+...+ a p sp= A 1 s- s 1 + A 2 s- s 2 +...+ A p s- s p H a s b 0 b 1 s b 2 s 2 ... b p s p 1 a 1 s a 2 s 2 ... a p s p A 1 s s 1 A 2 s s 2 ... A p s s p which implies h a t= A 1 s 1 t+ A 2 s 2 t+...+ A p s p tut h a t A 1 s 1 t A 2 s 2 t ... A p s p t u t For impulse invariance, we desire hn= h a nT= A 1 s 1 nT+ A 2 s 2 nT+...+ A p s p nTun h n h a n T A 1 s 1 n T A 2 s 2 n T ... A p s p n T u n Since A k s k Tnun A k zz- s k T A k s k T n u n A k z z s k T where |z|>| s k T| z s k T , and Hz=k=1p A k zz- s k T H z k 1 p A k z z s k T where |z|>maxk{| s k T|} z k s k T .
This technique is used occasionally in digital simulations of analog filters.
Problem 1
What is the main problem/drawback with this design technique?
[ Click for Solution 1 ]
Solution 1
Since it samples the non-bandlimited impulse response of the analog prototype filter, the frequency response aliases. This distorts the original analog frequency and destroys any optimal frequency properties in the resulting digital filter.
[ Hide Solution 1 ]

Comments, questions, feedback, criticisms?

Send feedback